几何非线性混合应变元的构造及应用

本文基于由文献〔１〕导出的几何非线性混合应变元一般公式，构造了三个八节点六面体几何非线性混合应变元和Ｓｉｍｏ－Ｒｉｆａｉ的二维四边形线性应变元的几何非线性混合应变元。数值结果表明，所构造的二维及三维几何非线性混合应变元具有理想的性能。它们通过分片试验，且没有虚假剪切现象和不可压缩材料的自锁。同时，它们对歪扭网格不敏感，在利用粗疏网格离散时对线性和非线性（几何和材料）问题具有很高的精度。

CONSTRUCTION OF MIXED STRAIN ELEMENTS IN GEOMETRICAL NONLINEARITY AND APPLICATIONS

Based cm the general formulations of the mixed strain element in geometrical nonlincarily derived in (1). Three eight noded hcxahcdral mixed strain elements and geometrically nonlinear versions ol quadrilateral mixed strain elements by Simo and Rifai are eonstrueled. Numerical results are presented to show that the resulting 2D and 3D geometrically nonlinear mixed strain elements possess all the ideal qualities. They are able to pass the patch lest, do not exhibit the false shear phenomena and do not lock for nearly incompressible materials. In addition, they are less sensitive to distorted meshes and exhibit high accuracy for both linear and geometrically and materially nonlinear problems, permitting coarse discretisations to be utilized.